I hate such workarounds so I've decided to dig deeper. While none of the available Ionic lifecycle hooks works in that case there are also Angular lifecycle hooks. It turns out that ngAfterViewChecked is the one I was looking for:

ngAfterViewChecked() {
this.myInput.setFocus()
}

So that is clean setFocus() solution for Ionic without using setTimeout() workaround.

Sidenote

In order to be able to refer to the input element with this.myInput you have to define it inside your Component as a ViewChild.

Here is the example of Modal Component which will autofocus its input after showing itself on the page.
Javascript: